Finite Group Databasebeta

← #484×D43 #19144497

Subgroups — #484×D43 #19144497

Order 5504.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D43C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3#14583236C212yesmaximal, complemented
4#14583235C211yesmaximal, characteristic, complemented
5#14583234C211yesmaximal, characteristic, complemented
6#14583233C212yesmaximal, complemented
7#14583232C211yesmaximal, characteristic, complemented
8#107×D43C212yesmaximal, complemented
9#103×D43C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic
11C43×#484C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C22×C4×D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×C8×D43C2212yes—
16#13063305C2211yescharacteristic
17#13063304C2211yescharacteristic
18#13063303—21no—
19#13063302—21no—
20#13063301C2211yescharacteristic
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4—21no—
23C4⋊C4×D43—21no—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C4⋊C4×D43C2212yes—
27C4⋊C4×D43C2212yes—
28C4⋊C4×D43C2211yescharacteristic
29C22⋊C4×D43—21no—
30#13063259C2212yescomplemented
31#13063258C2212yescomplemented
32#13063258C2212yescomplemented
33#13063250C2212yescomplemented
34#13063249C2212yescomplemented
35#13063248C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yes—
38C22⋊Q8×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43D411yescharacteristic
44C2×Q8×C43C2311yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C22×Dic43—21no—
48C22×Dic43D411yescharacteristic
49Q8×D43—24no—
50C2×C4×D43—24no—
51C2×C4×D43—21no—
52C2×C4×D43—21no—
53C2×C4×D43—22no—
54C2×C4×D43—22no—
55C2×C4×D43—44no—
56C2×C4×D43D411yescharacteristic
57C2×C4×D43D411yescharacteristic
58C2×C4×D43C2311yescharacteristic
59C2×C4×D43C2311yescharacteristic
60C2×Dic86—21no—
61C2×Dic86C2311yescharacteristic
62C2×C8×C43C2312yes—
63C4⋊C4×C43—21no—
64C4⋊C4×C43—21no—
65C4⋊C4×C43C2312yes—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C22⋊Dic43—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71C4⋊Dic43—21no—
72C4⋊Dic43—21no—
73C4⋊Dic43C2312yes—
74C4⋊Dic43C2311yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—22no—
77Dic43⋊C4—22no—
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80C2×C43⋊C8C2312yes—
81C8×D43—24no—
82C23×C43C2×D411yescharacteristic
83C22×D43—22no—
84C22×D43—22no—
85C22×D43Q1614yes—
86C22×D43C2×D411yescharacteristic
87C22×D43C2×D411yescharacteristic
88Q8×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—42no—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2411yescharacteristic
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—42no—
101C2×Dic43C2×D411yescharacteristic
102C2×Dic43C2×D411yescharacteristic
103C4×D43—22no—
104C4×D43—22no—
105C4×D43—22no—
106C4×D43—44no—
107C4×D43—42no—
108C4×D43—42no—
109C4×D43—44no—
110C4×D43#4114yes—
111Dic86—22no—
112Dic86—42no—
113C8×C43—22no—
114C43⋊C8—22no—
115C22×C43—21no—
116C22×C43—21no—
117C22×C43C2×Q1612yes—
118C22×C43C22×D411yescharacteristic
119C2×D43—21no—
120C2×D43—21no—
121C2×D43—28no—
122C2×D43#12312yes—
123C2×D43C2×Q1612yes—
124C2×D43C2×Q1612yes—
125C2×D43AGL(1,ℤ/8)12yes—
126C4×C43—21no—
127C4×C43—41no—
128C4×C43—42no—
129C4×C43—41no—
130C4×C43C2×#4112yes—
131Dic43—21no—
132Dic43—41no—
133Dic43—42no—
134Dic43—41no—
135Dic43#12312yes—
136C2×#484—431nomaximal, Sylow
137C2×C43—22no—
138C2×C43C2×#12311yescharacteristic
139C2×C43C22×Q1611yescharacteristic
140C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
141D43—22no—
142D43#48414yesdirect product factor
143C2×C22⋊Q8—431no—
144C22×C4⋊C4—431no—
145#484—431no—
146#484—431no—
147#484—432no—
148#484—432no—
149#484—431no—
150#484D4311yescharacteristic, direct product factor
151C2×#107—432no—
152C2×#103—432no—
153C2×C22⋊C8—431no—
154C43C2×#48411yescharacteristic, complemented, Sylow
155C22×Q8—431no—
156C23×C4—431no—
157C23×C4—861no—
158C22×C8—432no—
159C22⋊Q8—431no—
160C22⋊Q8—431no—
161C22⋊Q8—431no—
162C22⋊Q8—861no—
163C22⋊Q8—861no—
164C22⋊Q8C2×D4311yescharacteristic
165C2×C4⋊C4—431no—
166C2×C4⋊C4—432no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—431no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4—861no—
171C2×C4⋊C4—861no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4C2×D4311yescharacteristic
174C2×C22⋊C4—861no—
175#107—432no—
176#107—432no—
177#107—432no—
178#107C2×D4312yescomplemented
179#103—432no—
180#103—432no—
181#103—432no—
182#103C2×D4312yescomplemented
183C22⋊C8—431no—
184C22⋊C8—432no—
185C22⋊C8C2×D4311yescharacteristic
186C24—431no—
187C2×Q8—431no—
188C2×Q8—861no—
189C2×Q8—864no—
190C2×Q8C22×D4311yescharacteristic
191C22×C4—21no—
192C22×C4—431no—
193C22×C4—431no—
194C22×C4—431no—
195C22×C4—431no—
196C22×C4—431no—
197C22×C4—864no—
198C22×C4—861no—
199C22×C4—861no—
200C22×C4—862no—
201C22×C4—862no—
202C22×C4—861no—
203C22×C4—1724no—
204C22×C4C22×D4311yescharacteristic
205C2×C8—432no—
206C2×C8—864no—
207C2×C8C22×D4312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—432no—
211C4⋊C4—431no—
212C4⋊C4—862no—
213C4⋊C4—862no—
214C4⋊C4—861no—
215C4⋊C4—861no—
216C4⋊C4—861no—
217C4⋊C4—861no—
218C4⋊C4—861no—
219C4⋊C4C22×D4312yes—
220C4⋊C4C22×D4311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—861no—
223C22⋊C4—861no—
224C22⋊C4—861no—
225C23—431no—
226C23—434no—
227C23—431no—
228C23—862no—
229C23—862no—
230C23D4×D4311yescharacteristic
231Q8—22no—
232Q8—862no—
233Q8—1722no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—431no—
240C2×C4—434no—
241C2×C4—431no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—862no—
249C2×C4—1724no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1724no—
253C2×C4—1722no—
254C2×C4D4×D4311yescharacteristic
255C2×C4C23×D4311yescharacteristic
256C8—22no—
257C8—862no—
258C22—21no—
259C22—21no—
260C22—432no—
261C22—432no—
262C22—432no—
263C22—432no—
264C22—868no—
265C22—861no—
266C22—861no—
267C22Q16×D4312yes—
268C22C2×D4×D4311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—432no—
274C4—861no—
275C4—1721no—
276C4—1722no—
277C4—1721no—
278C4#41×D4312yes—
279C2—22no—
280C2—434no—
281C2—862no—
282C2#123×D4311yescharacteristic
283C2C2×Q16×D4311yescharacteristic
284C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43C2×#484
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14583236C2semidirect
4. #14583235C2semidirect
5. #14583234C2semidirect
6. #14583233C2semidirect
7. #14583232C2semidirect
8. #107×D43C2semidirect
9. #103×D43C2semidirect
11. C43×#484C2semidirect
30. #13063259C22semidirect
31. #13063258C22semidirect
32. #13063258C22semidirect
33. #13063250C22semidirect
34. #13063249C22semidirect
35. #13063248C22semidirect
40. #107×C43C22semidirect
41. #103×C43C22semidirect
142. D43#484direct (N × H)
150. #484D43direct (N × H)
154. C43C2×#484semidirect
178. #107C2×D43semidirect
182. #103C2×D43semidirect